Ordinary Differential Equations
E681630
Ordinary Differential Equations is a classic mathematical text that systematically develops the theory and methods for solving differential equations involving functions of a single variable, widely used in advanced undergraduate and graduate studies.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Ordinary Differential Equations canonical | 2 |
| Ordinary Differential Equations by Vladimir Arnold | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7685049 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ordinary Differential Equations Context triple: [Lev Pontryagin, notableWork, Ordinary Differential Equations]
-
A.
ODE
ODE is the state agency responsible for overseeing public education and implementing education policy in Oregon.
-
B.
Linear Differential Equations and Their Applications
"Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
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C.
Bernoulli differential equations
Bernoulli differential equations are a class of first-order nonlinear differential equations that can be transformed into linear form and are fundamental in the study of ordinary differential equations.
-
D.
Riccati equation
A Riccati equation is a type of nonlinear differential or difference equation, often quadratic in the unknown function, that plays a central role in control theory, filtering, and various areas of applied mathematics.
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E.
Cauchy problem
The Cauchy problem is a fundamental type of initial value problem in partial differential equations, where one seeks a solution satisfying prescribed data on a given initial surface.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ordinary Differential Equations Target entity description: Ordinary Differential Equations is a classic mathematical text that systematically develops the theory and methods for solving differential equations involving functions of a single variable, widely used in advanced undergraduate and graduate studies.
-
A.
ODE
ODE is the state agency responsible for overseeing public education and implementing education policy in Oregon.
-
B.
Linear Differential Equations and Their Applications
"Linear Differential Equations and Their Applications" is a classic mathematical text by Maxime Bôcher that systematically develops the theory of linear differential equations and demonstrates their use in solving applied problems.
-
C.
Bernoulli differential equations
Bernoulli differential equations are a class of first-order nonlinear differential equations that can be transformed into linear form and are fundamental in the study of ordinary differential equations.
-
D.
Riccati equation
A Riccati equation is a type of nonlinear differential or difference equation, often quadratic in the unknown function, that plays a central role in control theory, filtering, and various areas of applied mathematics.
-
E.
Cauchy problem
The Cauchy problem is a fundamental type of initial value problem in partial differential equations, where one seeks a solution satisfying prescribed data on a given initial surface.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
academic book
ⓘ
mathematics textbook ⓘ reference work ⓘ |
| aim |
presentation of methods for solving ODEs
ⓘ
systematic development of ODE theory ⓘ |
| audience |
applied scientists
ⓘ
engineering students ⓘ mathematics students ⓘ physics students ⓘ |
| contains |
algorithms for solving ODEs
ⓘ
illustrative applications ⓘ proofs ⓘ theorems ⓘ |
| discipline | mathematics ⓘ |
| educationalLevel |
advanced undergraduate
ⓘ
graduate ⓘ |
| field | ordinary differential equations ⓘ |
| hasFormat |
ebook
ⓘ
hardcover ⓘ paperback ⓘ |
| hasPart |
bibliographic references
ⓘ
exercises ⓘ theoretical expositions ⓘ worked examples ⓘ |
| language | English ⓘ |
| subdiscipline |
analysis
ⓘ
applied mathematics ⓘ |
| topic |
Green's functions
ⓘ
Laplace transform methods ⓘ boundary value problems ⓘ differential equations ⓘ eigenvalue problems ⓘ existence and uniqueness theorems ⓘ initial value problems ⓘ linear differential equations ⓘ nonlinear differential equations ⓘ numerical methods for differential equations ⓘ phase plane analysis ⓘ series solutions of differential equations ⓘ stability of solutions ⓘ sturm–liouville theory ⓘ systems of differential equations ⓘ |
| usedIn |
applied mathematics curricula
ⓘ
engineering curricula ⓘ physics curricula ⓘ university mathematics courses ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ordinary Differential Equations Description of subject: Ordinary Differential Equations is a classic mathematical text that systematically develops the theory and methods for solving differential equations involving functions of a single variable, widely used in advanced undergraduate and graduate studies.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
Lectures on Partial Differential Equations
→
relatedWork
→
Ordinary Differential Equations by Vladimir Arnold
ⓘ
linked to: Ordinary Differential Equations